The Problem With Dosage Calculation Used in Medicine
Executive Summary
- Dosage calculation is fraught with many more problems and inaccuracies than is generally understood.
Introduction
This article covers many of the common problems in drug dosage estimation and calculation.
- In this article, “estimation” refers to how the pharmaceutical company develops the dosage.
- The term “calculation” refers to how the drug dosage is eventually arrived at mathematically — which of course begins with the estimation.
The Dosage Calculation Issue
These quotes are from the article Medication Dispensing Errors and Prevention.
Dosage Calculation Problem #1: No Stated Duration of Treatment
In the past, some physicians would simply write down the total number of pills that a patient is supposed to get without specifying the duration of treatment. It is vital to specify the duration of treatment and that the duration of treatment matches the number of pills prescribed. When writing about the quantity of the drug, it is important to write down the actual number of pills (e.g., 90) rather than stating dispense for 2 months.
This is a major and continuing issue. People are placed on medications, but there is no duration estimate, and frequently, the use of the medicines continues for many years.
Another reason for specifying the number of doses is that it requires the patient to comply with follow-up and prevents them from just collecting older medications. If the patient has a chronic disorder, the practitioner should be treating each flare-up as a single event with a finite number of pills. If the patient has a flare-up or exacerbation, tell him or her to come to the clinic for an exam and, at that time, determine if more pills are needed. Just empirically prescribing pills for a theoretical recurrence only leads to confusion and a high risk of adverse reactions.
Remaining alert for high-risk medications. For example, if a patient has a deep vein thrombosis or a prosthetic heart valve and requires warfarin, only prescribe for 4 weeks at a time and reassess the patient on each visit. Do not give warfarin for many months at a time. The patient needs to be monitored for the INR, and the dose may have to be adjusted.
This is particularly problematic for dangerous drugs like Wayfarin, yet it is common for people to be on Warfarin for years.
Dosage Calculation Problem #2: Adjusting for the Liver and Kidney Function of the Patient
Liver and kidney function: Another widespread reason for medication errors is not considering renal or liver failure.
Patients with renal and liver dysfunction need lower doses. Otherwise, toxicity can result because of the failure to excrete or break down the medication.
Naturally, any reduced liver and or kidney function.
This is covered in the quote from the article Dose adjustment in patients with liver disease.
Unfortunately, there is no endogenous marker for hepatic clearance that can be used as a guide for drug dosing.
In order to predict the kinetic behaviour of drugs in cirrhotic patients, agents can be grouped according to their extent of hepatic extraction. For drugs with a high hepatic extraction (low bioavailability in healthy subjects), bioavailability increases and hepatic clearance decreases in cirrhotic patients.
Dosage Calculation Problem #3: The Problem With Similar Sounding Drug Names
There have been many new drug releases in the last decade, and generics with similar names have flooded the market. In addition to having similar names, many of these medications have multiple uses and alternative names. If the diagnosis is not stated on the prescription, there is a risk that the drug may be prescribed for too long or an inadequate amount of time. With dozens of new generics with similar names, the risk of error is very high. To counter the consequences of unintended substitutions for medications, the US Pharmacopeia has listed the names of look-alike medications, and the ISMP has developed a list of abbreviations that are routinely misinterpreted.
The following quotes are from the article Medication Dispensing Errors and Prevention.
Dosage Calculation Problem #4: Quality Checks Are Performed by the Pharmacist
Dosage checking would best be performed by pharmacists, who perform dosage calculations significantly better than physicians and nurses.
Interestingly, the pharmacist checks the quality of the overall process.
Dosage Calculation Problem #5: Sex Differences in Dosages
These quotes are from the article Sex differences in pharmacokinetics predict adverse drug reactions in women.
The Lower Levels of Women Used in Clinical Trials
A consequence of this sex inequality hides in plain sight today: most drugs are prescribed to women and men at the same dose. Many currently prescribed drugs were approved by the US Food and Drug Administration (FDA) prior to 1993, with inadequate enrollment of female animals in preclinical research and of women in clinical trialclinical trial.
An illustrative example is found in the sedative-hypnotic drug zolpidem, which has been marketed under several names (e.g., Ambien, Edluar, Zolpimist) since it was first approved by the FDA, 1 year before the NIH Revitalization Act.
This is the issue with having so many copycat drugs.
Only after decades of post-marketing reports of cognitive deficits in women given the standard male dose were sex-based dose adjustments development.
This is quite amazing. And why didn’t the drug company know that women were being overdosed — because drug companies don’t like having many women in clinical trials for their drugs? But they very much like selling their medications to women after the clinical trials are complete, and they have estimated a dosage for men only.
Men are viewed as easier to manage in clinical trials — but of course, when the drug is approved, it is rolled out to both men and women. Women who were driven into cognitive deficit by taking the male-optimized dosage of Zolpidem can expect to get no apologies from Mylan, Teva, Roxane, Watson, Ranbaxy, Dr. Reddy’s Laboratories, Apotex, Synthon Pharmaceuticals, Genpharm, Mutual Pharmaceutical, Caraco, Carlsbad Technology, and Lek Pharmaceuticals.
Higher Adverse Events in Part Due to Overdosing
Women have a nearly 2-fold greater risk than men for exhibiting ADRs across all drug classes and are significantly more likely to be hospitalized secondary to an ADR. In general, drug disposition occurs through separate phases: absorption, distribution, bioavailability, metabolism, and excretion, and sex differences have been documented for each phase.
Reasons Women Process Drugs Differently From Men
Women generally have a lower body weight and organ size and a higher percentage of body fat, which affects the absorption and distribution of drugs. Women have a slower gastric emptying time and lower gastric pH, lower plasma volume, body mass index, average organ blood flow, and total body water differences, all of which affect drug distribution and PKs]. Responses to drugs are also affected by physiological changes during the menstrual cycle. The striking hormonal variations across days over the course of the human menstrual have no parallel in men in which hormonal variations largely occur within rather than across days].
Drug Excretion Speed Differences in Women Versus Men
The anticoagulant drug lepirudin is excreted by the kidney with systemic clearance in women about 25% lower than in men. But PK variables do not translate linearly into phenotypes; thus, in women lepirudin is detectible in the circulation for up to 48 h, compared to just 2 h in men, which greatly increases the potential for undesired bleeding; indeed, in this example, low molecular weight heparin-induced thrombocytopenia is a clinically important ADR which occurs more frequently in women than men, a difference that corresponded to much higher drug expodure as indicated by female-bias in multiple PK measures.
This leads directly to the next problem with dosage calculation as currently practiced.
Dosage Calculator Problem #6: The Lack of Weight-Based Dosages
Most drugs are not administered on a milligram/kilogram basis but as a “one size fits all” dose, leading to higher exposures in women.
And, of course, higher exposures for smaller and lighter people.
It is amazing to see such differently sized people with different blood volumes and organ sizes using the same prescription. This area illustrates the inaccuracy of modern medical dosage calculations. One has to wonder how a drug can be prescribed without accounting for weight, which is addressed in the following quote.
Under optimal circumstances, the dose should be based on milligram/kilogram body weight, or titrated to the desired clinical effect.
Correction for height, weight, surface area, or body composition eliminates a minority of sex-dependent PK differences.
I noticed this when I began creating the dosage calculators, which showed that most drug dosages are not weight dependent, which makes little sense. The response from the medical establishment is to do nothing on the topic and to keep the same dose for men and women, and in fact, to hide this issue from the public.
This leads to the next problem with dosage calculation, which is currently practiced.
Dosage Calculation Problem #7: Inefficient and Error Prone Calculation
It is amazing that nurses are still calculating dosages through formulas rather than online calculators.
This is explained in the quote from the article Drug Calculations: How to Use the Universal Formula.
Universal Formula (Toney-Butler, 2021)
In the universal formula (or “desired over have method”), the desired amount (D) is the dose prescribed and the amount on hand (H) or the amount you “have” is the available dose or concentration. The quantity (Q) is the form and amount in which the drug is supplied (i.e. tablet, capsule, liquid). To calculate the dose, take the desired amount and divide it by the amount on hand, then multiply it by the quantity, like this:
An order for digoxin 0.5 mg IV daily is placed. Digoxin 0.25 mg/mL is available from the pharmacy. How many mL will you need to administer a 0.5 mg dose?
.5 MG /.25 MG x 1 ML = 2ML
The fact that nearly all dosages are still calculated this way means that very little is included in the calculation that provides scaling that makes the dosage more accurate.
This causes drug companies to develop very simplified dosage estimations. As has been addressed already, it is rare even to find weight-based dosages.
But if we take the example of alcohol, larger people obviously will consume more alcohol than smaller people. They have larger organs – particularly a larger liver and larger kidneys, a larger blood volume, and more muscle that consumes or metabolizes the drug. Therefore, how can medications so rarely be weight-based?
Notice the following quote, which is advice to nurses performing drug dosage calculations.
- Check that your answer makes sense clinically.
- Triple check your work.
- Have a colleague or pharmacist check your work.
- Know general therapeutic drug doses for commonly administered medications.
Why would medicine still ask nurses to calculate dosages like this when automating the process with online calculators is so easy? The dosage calculator can be checked for accuracy before it is rolled out for nurses or published, and then it is highly reliable and will give the same output given the same input.
In that case, the only potential for error is if inaccurate inputs (weight, sex, etc..) are applied. This is another area for error, but the potential for error is greatly reduced.
The types of errors that these bullet points are designed to stop are already worked out a single time in an online dosage calculator.
As I already stated, weight-based dosages are rare for self-administered pills. However, they are typical for IV drips and, again, are the responsibility of the nurse to calculate.
See this quote from the article Drug Calculations: How To Use Dimensional Analysis.
Dimensional analysis (DA) or factor-label method uses a series of conversion factors of equivalency from one system of measurement to another but doesn’t require memorizing specific formulas. This method reduces errors and can be used for all dosage calculations.
To set up the equation, start with the label or unit of measure needed in the answer.
Build the equation by placing information with the same label as the preceding denominator in the numerator so that unwanted labels will cancel out. Repeat until all units of measure not needed in the answer are cancelled out.
Calculate to determine the correctly labeled numeric answer. Don’t round any numbers in the equation until you have the final answer.Let’s take a look an example to illustrate this method.
Example: IV Dose
Administer digoxin 0.5 mg IV daily. The drug concentration available from the pharmacy is digoxin 0.25 mg/mL. How many mL will you need to administer a 0.5 mg dose?Step 1: What unit of measure (label) is needed? Place this on the left side of the equation
Step 2: On the right side, place the information given with the same label needed in the numerator. In this example, we know that the drug concentration available is 0.25 mg/mL. Place mL in the numerator and 0.25 mg in the denominator.
Step 3: The desired dose is 0.5 mg. Place information with the same label as the preceding denominator into the equation in the numerator to cancel out the unwanted labels. Repeat this step sequentially until all unwanted labels are canceled out.
Step 4. Multiply numbers across the numerator, then multiply all the numbers across the denominator. Divide the numerator by the denominator for the final answer with the correct label.
- Again — why, with computers and websites and with the technology available, are things still being done this way?
- How much nursing time is being taken up by having nurses do this, and how many inaccurate dosages are being administered — and therefore, medical errors are being produced using this approach?
Dosage Calculation Problem #8: How The Obese Are Normally Excluded from Clinical Trials
Obese people are generally excluded from clinical trials as it adds complications to the clinical trial, and pharmaceutical companies select the most healthy test subjects to make their trials look as successful as possible. However, the problem arises when the drug is rolled out to the public, and as a high percentage of the population is obese or has generally high body fat, the dosage that has been tested only on normal-weight individuals is then applied to a substantial obese population.
Dosage Calculation Problem #9: Drugs Have Different Active Pharmaceutical Ingredients
Different versions of drugs have different active pharmaceutical ingredients. The issue of excipients interacting with the API is another topic, but I will hold that to the side for now.
The worst-case scenario for this Africa is that Africa is the dumping ground for the lowest-quality pharmaceuticals manufactured by Indian companies. Drugs that fail quality testing are not destroyed but usually sent and sold to Africa — at a much-reduced price. They do this because the drug companies no that African countries have no drug oversight, and they can’t get into trouble.
Many African MDs have noticed this; therefore, many have adjustment tables. Sometimes, the dosages given in Africa are 3 or 4 times greater than those used in the US or Europe. The reason is that the drug has that much less active pharmaceutical ingredient.
With an online calculator, this adjustment to the dosage can be addressed with a single drop-down to change the manufacturer’s location.
Conclusion
I never worked as a nurse and only began to investigate this topic after developing dosage calculators for Brightwork that subscribers would use. In order to enhance these calculators, it led me to investigate the topic, and what I found was surprising. Dosage estimation calculation is something that I don’t think a lot of people give a lot of thought to. When they get the dosage from their pharmacist and assume it’s right. However, some quite blatant oversimplifications become apparent once you look into “how the sausage is made” regarding drug doses being created upstream. And then the way in which even the calculation to what is often a dosage that is very generalized and not specific to the person or to the drug’s source of manufacturer and that variance also becomes apparent.
Here are some rather obvious conclusions on this topic.
- There is very good reason to think that many side effects or adverse events are made worse by the present dosage estimation and calculation approach.
- On the other side, there is a significant percentage of doses that are too low — although it seems more likely that the majority are too high — something which overwhelmingly applies to women and girls, given how dosage estimations are performed in the first place. This also applies to the obese.
- The onerous calculation of dosage by nurses is both a source of significant medical errors and a significant waste of large nursing resources—a profession that is perpetually understaffed. Something else that I don’t see mentioned is that nursing is considered a high-stress job—although naturally, the stress level varies greatly depending on the specific area of nursing. Being under stress is not a good situation for performing calculations. In fact, being asked to perform high negative consequence calculations under stress creates further stress. Given the level of stress at the clinical environment nurses can be forced into more calculation errors than they would otherwise make.
Reviewing Currently Available Online Drug Dosage Calculators
I spent time testing what I propose as a much better approach: online dosage calculators. I tested a number of these calculators and found quite a few of them difficult to use and low in multidimensionality. One was on MD Anderson’s website, and I found it quite amateurish. The term “cobbled together at the last minute” comes to mind. What is interesting about this is MD Anderson once gave a journalist going for treatment four times the standard dose of a chemotherapy drug, quickly killing her. This seems like something that MD Anderson and other cancer centers would want to get right.
This gets to a core execution issue, which I have found repeatedly: medicine is generally far lower in math proficiency and attention to detail than one would naturally guess, particularly considering that medicine frequently boasts about how its MDs are some of society’s best-educated and highest-intelligence members. Here are several examples of this math issue.
The Lack of Medical Cost Benefit Analysis
As I have addressed in numerous articles at this site, medicine has virtually no cost-benefit analysis performed on individual treatments.
A drug is normally recommended based upon the benefit to the pharmaceutical company, hospital, or MD, and of course, whether the insurance company has agreed to reimburse the cost rather than any analysis of the cost and benefit to the patient.
Oversights on the Mathematical Basics of Medicine: The Problematic Medical Orientation Around Dosage Estimation
When we get to more of the “blocking and tackling” mathematics—something like dosage calculation—once again, medicine prefers not to get into sufficient detail. It is simply easier for the medical establishment to use averages. Still, these averages, for example, result in overdosing for women and a high percentage of adverse drug events for women.
I can say with confidence that medicine greatly underemphasizes the mathematical aspects of care. This has resulted in a dramatic underinvestment in online calculators that could simplify and increase the quality of dosage calculation.
This problem has existed since the beginning of medicine and now looks quite antiquated, given the available technologies. Furthermore, as people in many countries are taking more pharmaceuticals than at any time in human history, the problems in this area are exacerbated.
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